Theorems · Theorem · logic and foundations
Set.Finite.card_lt_card
∀ {α : Type u_1} {s t : Set α}, t.Finite → s ⊂ t → Nat.card ↑s < Nat.card ↑t- Defined in
- Mathlib.SetTheory.Cardinal.NatCard
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Fintypeproof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Set.Finitestatement and proof · cited by 1,814
- Nat.cardstatement · cited by 844
- Set.Finite.subsetproof · cited by 285
- Nat.card_eq_fintype_cardproof · cited by 200
- Set.Finite.fintypeproof · cited by 38
- Set.card_lt_cardproof · cited by 2
- subset_of_ssubsetproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Set.Finite.eq_of_subset_of_card_leproof · cited by 4
- OrderedFinpartition.one_lt_partSize_index_zeroproof · cited by 0
- Set.Finite.card_strictMonoOnproof · cited by 0
- Set.card_strictMonoproof · cited by 0